ISO/FDIS 31657-3
(Main)Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 3: Characteristic values for calculation of tilting pad journal bearings
Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part 3: Characteristic values for calculation of tilting pad journal bearings
This document specifies the characteristic values for selected tilting-pad journal bearings with four or five centrally or eccentrically supported tilting pads and with angular spans of pad sliding surfaces of Ω = 80°, 60° and 45°. The functions plotted and listed in table form below are required for the operationally safe design of hydrodynamic tilting-pad journal bearings according to ISO/TS 31657-1. They are based on the presumptions and boundary conditions indicated there and only apply to stationary operating states. The symbols used are explained in ISO/TS 31657-1; calculation examples are also included there. The calculation method described in ISO/TS 31657-1 can also be used for other tilting-pad journal bearing designs, if the numerical solutions of the basic equations are available in the same manner for these designs.
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Part 3:
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Characteristic values for calculation
of tilting pad journal bearings
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Reference number
FINAL DRAFT
International
Standard
ISO/TC 123/SC 8
Plain bearings — Hydrodynamic
Secretariat: JISC
plain journal bearings under
Voting begins on:
steady-state conditions —
Part 3:
Voting terminates on:
Characteristic values for calculation
of tilting pad journal bearings
RECIPIENTS OF THIS DRAFT ARE INVITED TO SUBMIT,
WITH THEIR COMMENTS, NOTIFICATION OF ANY
RELEVANT PATENT RIGHTS OF WHICH THEY ARE AWARE
AND TO PROVIDE SUPPOR TING DOCUMENTATION.
© ISO 2025
IN ADDITION TO THEIR EVALUATION AS
All rights reserved. Unless otherwise specified, or required in the context of its implementation, no part of this publication may
BEING ACCEPTABLE FOR INDUSTRIAL, TECHNO-
LOGICAL, COMMERCIAL AND USER PURPOSES, DRAFT
be reproduced or utilized otherwise in any form or by any means, electronic or mechanical, including photocopying, or posting on
INTERNATIONAL STANDARDS MAY ON OCCASION HAVE
the internet or an intranet, without prior written permission. Permission can be requested from either ISO at the address below
TO BE CONSIDERED IN THE LIGHT OF THEIR POTENTIAL
or ISO’s member body in the country of the requester.
TO BECOME STAN DARDS TO WHICH REFERENCE MAY BE
MADE IN NATIONAL REGULATIONS.
ISO copyright office
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Phone: +41 22 749 01 11
Email: copyright@iso.org
Website: www.iso.org
Published in Switzerland Reference number
ii
Contents Page
Foreword .iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Characteristic values for calculation of multi-lobed journal bearings . 1
4.1 General .1
4.2 Tilting-pad journal bearings with four tilting pads .4
4.3 Tilting-pad journal bearings with five tilting pads . 39
Annex A (informative) Characteristic curves for tilting-pad bearings with five pads .62
Bibliography .73
iii
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards
bodies (ISO member bodies). The work of preparing International Standards is normally carried out through
ISO technical committees. Each member body interested in a subject for which a technical committee
has been established has the right to be represented on that committee. International organizations,
governmental and non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely
with the International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types
of ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent
rights in respect thereof. As of the date of publication of this document, ISO had not received notice of (a)
patent(s) which may be required to implement this document. However, implementers are cautioned that
this may not represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents. ISO shall not be held responsible for identifying any or all such patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
This document was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 8,
Calculation methods for plain bearings and their applications.
This first edition of ISO 31657-3 cancels and replaces ISO/TS 31657-3:2020, which has been technically
revised.
The main changes are as follows:
— the title has been modified;
— Figure 1 has been updated.
A list of all parts in the ISO 31657 series can be found on the ISO website.
Any feedback or questions on this document should be directed to the user’s national standards body. A
complete listing of these bodies can be found at www.iso.org/members.html.
iv
FINAL DRAFT International Standard ISO/FDIS 31657-3:2025(en)
Plain bearings — Hydrodynamic plain journal bearings under
steady-state conditions —
Part 3:
Characteristic values for calculation of tilting pad journal
bearings
1 Scope
This document specifies the characteristic values for selected tilting-pad journal bearings with four or five
centrally or eccentrically supported tilting pads, and with angular spans of pad sliding surfaces of Ω = 80°,
60° and 45°.
2 Normative references
The following documents are referred to in the text in such a way that some or all of their content constitutes
requirements of this document. For dated references, only the edition cited applies. For undated references,
the latest edition of the referenced document (including any amendments) applies.
ISO 31657-1:2025, Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions — Part
1: Calculation of multi-lobed and tilting pad journal bearings
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
— ISO Online browsing platform: available at https:// www .iso .org/ obp
— IEC Electropedia: available at https:// www .electropedia .org/
4 Characteristic values for calculation of multi-lobed journal bearings
4.1 General
The characteristic values plotted and listed in this clause are required for the operationally safe design
of hydrodynamic tilting-pad journal bearings in accordance with ISO 31657-1. They are based on the
presumptions and boundary conditions indicated there and only apply to stationary operating states. The
symbols used shall be in accordance with ISO 31657-1:2025, Table 1; calculation examples are also given in
ISO 31657-1:2025, Annex A.
The calculation method described in ISO 31657-1 can also be used for other tilting-pad journal bearing
designs, if the numerical solutions of the basic equations are available in the same manner for these designs.
NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked
against acceptable conditions. Another calculation procedure is equally admissible.
The characteristic values for symmetrically loaded tilting-pad journal bearings with four and five centrally
*
(relative angular distance between leading edge and pivot position of pad Ω = 0,5) or eccentrically (
F
*
Ω = 0,6) supported tilting pads are indicated.
F
The characteristic values were calculated for the geometrical parameters summarised in Figure 1 (angular
spans of pad sliding surface Ω, angular coordinates of pivot position of pad ϕ , profile factors K , bearing
F,1 P
* *
width ratios B ) in the operating range 0,02 ≤ h ≤ 1. The following (dimensionless) characteristic values
min
are individually listed from Tables 1 to 56:
a) Static characteristic values
The Sommerfeld number is given as Formula (1):
F⋅ψ
eff
So= (1)
BD⋅⋅ηω⋅
eff
The relative eccentricity is given as Formula (2):
e
ε = (2)
C
Re, ff
Attitude angle β in °C.
For the product of maximum lubricant film pressure parameter and Sommerfeld number, see
Formula (3):
p ·ψ
* maxeff
pS· o= (3)
max
ηω⋅
eff
For the minimum relative lubricant film thickness, see Formula (4):
h
* min
h = (4)
min
C
Re, ff
For the friction force parameter, see Formula (5):
f
*
F =⋅So (5)
f
ψ
eff
For the lubricant flow rate parameter due to hydrodynamic pressure build-up, see Formula (6):
Q
* 3
Q = (6)
Q
For the lubricant flow rate parameter due to supply pressure, see Formula (7):
Q
p
*
Q = (7)
p
*
PQ⋅
en 0
For the lubricant flow rate parameter at the exit of the lubricant gap, see Formula (8):
Q
*
Q = (8)
Q
For non-dimensional difference between maximum temperature of lubricant film and lubricant
temperature in the lubricant pocket, see Formula (9):
ρψ⋅⋅c
peff
*
ΔT = ·ΔT (9)
max max
pf⋅
b) Dynamic characteristic values
For non-dimensional lubricant film stiffness coefficients, see Formula (10):
ψ
* eff
c = ⋅c (i, k = 1, 2) (10)
ik, ik,
2⋅⋅B ηω⋅
eff
For non-dimensional lubricant film damping coefficients, see Formula (11):
ψ
* eff
d = ⋅⋅ω d (i, k = 1, 2) (11)
ik, ik,
2⋅⋅B ηω⋅
eff
*
For some selected tilting-pad journal bearings (Ω = 0,6, Ω = 45°, ϕ = 36°), these characteristic
F F,1
values are shown graphically as a function of the Sommerfeld number, So, and the profile factor, K in
P
Annex A, Figures A.1 to A.11.
Figure 1 — Geometrical parameters of selected tilting-pad journal bearings
* *
(ΩΩ = 0,5 andΩΩ = 0,6)
F F
4.2 Tilting-pad journal bearings with four tilting pads
The characteristic values for tilting-pad journal bearings with four centrally or eccentrically supported
tilting pads and angular spans of pad sliding surface of Ω = 80° or 60° are given in Tables 1 to 34.
*
Table 1 — Characteristic values of a tilting-pad bearing with four centrally (ΩΩ = 0,5) supported tilting pads (Ω = 80°, φ = 45°, K = 2,
F F,1 P
B* = 0,5)
* * * * * * * * * * * * * * *
So ε β [°]
pS⋅ o h F Q Q Q ΔT c c c c d d d d
max min f 3 P 2 max 11 12 21 22 11 12 21 22
0,000 0,000 0,00 0,278 0,829 2,785 0,909 0,000 1,730 1,02 0,283 0,000 0,000 0,283 0,335 0,000 0,000 0,335
0,021 0,050 0,00 0,308 0,796 2,789 0,909 0,000 1,730 1,10 0,286 0,000 0,000 0,286 0,337 0,000 0,000 0,337
0,042 0,100 0,00 0,342 0,763 2,800 0,907 0,000 1,730 1,18 0,295 0,000 0,000 0,295 0,342 0,000 0,000 0,342
0,086 0,200 0,00 0,426 0,698 2,846 0,902 0,000 1,732 1,36 0,330 0,000 0,000 0,330 0,362 0,000 0,000 0,362
0,136 0,300 0,00 0,539 0,632 2,925 0,893 0,000 1,735 1,58 0,397 0,000 0,000 0,397 0,399 0,000 0,000 0,399
0,197 0,400 0,00 0,692 0,567 3,043 0,881 0,000 1,739 1,84 0,505 0,000 0,000 0,505 0,456 0,000 0,000 0,456
0,273 0,500 0,00 0,907 0,503 3,210 0,863 0,000 1,744 2,15 0,678 0,000 0,000 0,678 0,546 0,000 0,000 0,546
0,374 0,600 0,00 1,216 0,440 3,436 0,841 0,000 1,752 2,51 0,954 0,000 0,000 0,954 0,686 0,000 0,000 0,686
0,512 0,700 0,00 1,674 0,378 3,741 0,812 0,000 1,760 2,93 1,403 0,000 0,000 1,403 0,905 0,000 0,000 0,905
0,713 0,800 0,00 2,392 0,317 4,157 0,776 0,000 1,773 3,51 2,167 0,000 0,000 2,167 1,253 0,000 0,000 1,253
1,023 0,900 0,00 3,587 0,259 4,735 0,732 0,000 1,788 4,34 3,562 0,000 0,000 3,562 1,841 0,000 0,000 1,841
1,245 0,950 0,00 4,501 0,230 5,111 0,707 0,000 1,796 4,88 4,707 0,000 0,000 4,707 2,299 0,000 0,000 2,299
1,541 1,000 0,00 5,768 0,202 5,568 0,679 0,000 1,806 5,65 6,389 0,000 0,000 6,389 2,931 0,000 0,000 2,931
1,943 1,050 0,00 7,584 0,174 6,134 0,648 0,000 1,816 6,49 8,951 0,000 0,000 8,951 3,848 0,000 0,000 3,848
2,512 1,100 0,00 10,311 0,147 6,850 0,613 0,000 1,829 7,76 13,077 0,000 0,000 13,077 5,241 0,000 0,000 5,241
3,358 1,150 0,00 14,651 0,121 7,787 0,575 0,000 1,842 9,64 20,191 0,000 0,000 20,191 7,500 0,000 0,000 7,500
4,708 1,200 0,00 22,167 0,095 9,074 0,532 0,000 1,857 12,41 33,852 0,000 0,000 33,852 11,308 0,000 0,000 11,308
7,086 1,250 0,00 36,774 0,070 10,96
...
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ISO/TC 123/SC 8
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Plain bearings — Hydrodynamic plain journal bearings under
steady-state conditions — —
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Characteristic values for calculation of tilting pad journal bearings
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ISO/DIS FDIS 31657-3:2024(E2025(en)
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or posting on the internet or an intranet, without prior written permission. Permission can be requested from either ISO
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at the address below or ISO’s member body in the country of the requester.
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ISO copyright office
CP 401 • Ch. de Blandonnet 8
CH-1214 Vernier, Geneva
Phone: + 41 22 749 01 11
EmailE-mail: copyright@iso.org
Website: www.iso.orgwww.iso.org
Published in Switzerland
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ⅳ © ISO 2024 2025 – All rights reserved
ii
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Contents
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Foreword . iv
stops: Not at 15.2 cm
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Characteristic values for calculation of multi-lobed journal bearings . 1
Annex A (informative) Characteristic curves for tilting-pad bearings with five pads . 66
Bibliography . 87
Foreword . iv
1 Scope . 1
2 Normative references . 1
3 Terms and definitions . 1
4 Characteristic values for calculation of multi-lobed journal bearings . 1
4.1 General . 1
4.2 Tilting-pad journal bearings with four tilting pads . 4
4.3 Tilting-pad journal bearings with five tilting pads . 41
Annex A (informative) Characteristic curves for tilting-pad bearings with five pads . 62
Bibliography . 73
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iii
ISO/DIS FDIS 31657-3:2024(E2025(en)
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Formatted: Font: Bold
Foreword
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ISO (the International Organization for Standardization) is a worldwide federation of national standards
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bodies (ISO member bodies). The work of preparing International Standards is normally carried out through Adjust space between Asian text and numbers
ISO technical committees. Each member body interested in a subject for which a technical committee has been
established has the right to be represented on that committee. International organizations, governmental and
non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the
International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.
The procedures used to develop this document and those intended for its further maintenance are described
in the ISO/IEC Directives, Part 1. In particular, the different approval criteria needed for the different types of
ISO documents should be noted. This document was drafted in accordance with the editorial rules of the
ISO/IEC Directives, Part 2 (see www.iso.org/directives).
Field Code Changed
Formatted: English (United Kingdom)
ISO draws attention to the possibility that the implementation of this document may involve the use of (a)
patent(s). ISO takes no position concerning the evidence, validity or applicability of any claimed patent rights
in respect thereof. As of the date of publication of this document, ISO had not received notice of (a) patent(s)
which may be required to implement this document. However, implementers are cautioned that this may not
represent the latest information, which may be obtained from the patent database available at
www.iso.org/patents.www.iso.org/patents. ISO shall not be held responsible for identifying any or all such
patent rights.
Any trade name used in this document is information given for the convenience of users and does not
constitute an endorsement.
For an explanation of the voluntary nature of standards, the meaning of ISO specific terms and expressions
related to conformity assessment, as well as information about ISO's adherence to the World Trade
Organization (WTO) principles in the Technical Barriers to Trade (TBT), see www.iso.org/iso/foreword.html.
Field Code Changed
Formatted: English (United Kingdom)
This document was prepared by Technical Committee ISO/TC 123, Plain bearings, Subcommittee SC 8,
Calculation methods for plain bearings and their applications.
This first edition of ISO 31657-3 cancels and replaces ISO/TS 31657-3:2020, which has been technically
Formatted: English (United Kingdom)
revised.
The main changes are as follows:
Formatted: Don't keep with next
Formatted: Font: Cambria, English (United Kingdom)
— — Titlethe title has been modified. ;
Formatted: List Continue 1
— Figure 1Figure 1 has been updated.
Formatted: List Continue 1, No bullets or numbering
Formatted: English (United Kingdom)
A list of all parts in the ISO 31657 series can be found on the ISO website.
Formatted: Adjust space between Latin and Asian text,
Any feedback or questions on this document should be directed to the user’s national standards body. A
Adjust space between Asian text and numbers
complete listing of these bodies can be found at www.iso.org/members.html.
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Formatted: Default Paragraph Font
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Formatted: English (United Kingdom)
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ⅳ © ISO 2024 2025 – All rights reserved
iv
Final DRAFT International Standard
Plain bearings — Hydrodynamic plain journal bearings under steady-
state conditions — —
Formatted: Main Title 2, Adjust space between Latin
Part 3:
and Asian text, Adjust space between Asian text and
Characteristic values for calculation of tilting pad journal bearings
numbers
1 Scope
This document specifies the characteristic values for selected tilting-pad journal bearings with four or five
centrally or eccentrically supported tilting pads, and with angular spans of pad sliding surfaces of Ω = 80°, 60°
and 45°.
2 Normative references
Formatted: Default Paragraph Font
Formatted: RefNorm, Adjust space between Latin and
The following documents are referred to in the text in such a way that some or all of their content constitutes
Asian text, Adjust space between Asian text and
requirements of this document. For dated references, only the edition cited applies. For undated references,
numbers
the latest edition of the referenced document (including any amendments) applies.
Formatted: Default Paragraph Font
ISO 31657--1:2025, Plain bearings — Hydrodynamic plain journal bearings under steady-state conditions —
Formatted: Default Paragraph Font
Part 1: Calculation of multi-lobed and tilting pad journal bearings
Formatted: Default Paragraph Font, Font: Italic
Formatted: Adjust space between Latin and Asian text,
3 Terms and definitions
Adjust space between Asian text and numbers, Tab
stops: Not at 0.7 cm + 1.4 cm + 2.1 cm + 2.8 cm +
No terms and definitions are listed in this document.
3.5 cm + 4.2 cm + 4.9 cm + 5.6 cm + 6.3 cm + 7 cm
Formatted: Adjust space between Latin and Asian text,
ISO and IEC maintain terminological databases for use in standardization at the following addresses:
Adjust space between Asian text and numbers
— — ISO Online browsing platform: available at https://www.iso.org/obphttps://www.iso.org/obp
Formatted: Adjust space between Latin and Asian text,
Adjust space between Asian text and numbers, Tab
— — IEC Electropedia: available at http://www.electropedia.org/https://www.electropedia.org/
stops: Not at 0.71 cm
Formatted: Adjust space between Latin and Asian text,
4 Characteristic values for calculation of multi-lobed journal bearings
Adjust space between Asian text and numbers
Formatted: Default Paragraph Font
4.1 General
Formatted: Default Paragraph Font
The characteristic values plotted and listed in this clause are required for the operationally safe design of
Formatted: Default Paragraph Font
hydrodynamic tilting-pad journal bearings in accordance with ISO 31657-1. They are based on the
Formatted: Default Paragraph Font
presumptions and boundary conditions indicated there and only apply to stationary operating states. The
symbols used are explainedshall be in accordance with ISO 31657-1:2025, Table 1; calculation examples are
Formatted: Default Paragraph Font
also given in ISO 31657-1:2025, Annex A.
Formatted: Default Paragraph Font
The calculation method described in ISO 31657-1 can also be used for other tilting-pad journal bearing Formatted: Default Paragraph Font
designs, if the numerical solutions of the basic equations are available in the same manner for these designs.
Formatted: Default Paragraph Font
Formatted: Default Paragraph Font
NOTE Equivalent calculation procedures exist that enable operating conditions to be estimated and checked against
acceptable conditions. Another calculation procedure is equally admissible.
Formatted: Default Paragraph Font
Formatted: Left, Space After: 0 pt, Line spacing: single
Formatted: Font: 11 pt
Formatted: HeaderCentered
Formatted: Font: Bold
The characteristic values for symmetrically loaded tilting-pad journal bearings with four and five centrally
Formatted: Adjust space between Latin and Asian text,
* *
∗
Adjust space between Asian text and numbers
(relative angular distance between leading edge and pivot position of pad 𝛺 = 0,5) or eccentrically (
F F F
∗
(𝛺 = 0,6) supported tilting pads are indicated.
F
The characteristic values were calculated for the geometrical parameters summarised in Figure 1Error!
Reference source not found. (angular spans of pad sliding surface Ω, angular coordinates of pivot position
* * ∗
∗
K
of pad ,𝜑 , profile factors ,𝐾 , bearing width ratios B )𝐵 ) in the operating range 0,02 ≤ h ℎ ≤ 1.
F,1 F,1 P min
P min
The following (dimensionless) characteristic values are individually listed from table 1Error! Reference
source not found. to 56:Error! Reference source not found.:
a) a) Static characteristic values
Formatted: Line spacing: single, Numbered + Level: 1
+ Numbering Style: a, b, c, … + Start at: 1 + Alignment:
The Sommerfeld number: is given as Error! Reference source not found.: Left + Aligned at: 0 cm + Indent at: 0 cm, Adjust space
between Latin and Asian text, Adjust space between
2 Asian text and numbers, Tab stops: Not at 0.63 cm +
F
eff
0.7 cm + 1.4 cm + 2.1 cm + 2.8 cm + 3.5 cm + 4.2
So
BD
cm + 4.9 cm + 5.6 cm + 6.3 cm + 7 cm
eff
Formatted: Adjust space between Latin and Asian text,
Relative eccentricity:
Adjust space between Asian text and numbers
e
C
R ,eff
𝐹⋅𝜓
eff
𝑆𝑜= (1)
𝐵⋅𝐷⋅𝜂 ⋅𝜔
eff
The relative eccentricity is given as Error! Reference source not found.:
𝑒
𝜀= (2)
𝐶
R,eff
Attitude angle β in C .°C.
Formatted: Adjust space between Latin and Asian text,
Adjust space between Asian text and numbers
ProductFor the product of maximum lubricant film pressure parameter and Sommerfeld number:, see
Error! Reference source not found.:
p ·
* max eff
p ·So
max
eff
𝑝 ·𝜓
max
∗ eff
Minimum𝑝 ·𝑆𝑜= (3)
𝑚𝑎𝑥
𝜂 ⋅𝜔
eff
For the minimum relative lubricant film thickness:, see Error! Reference source not found.:
Formatted: Adjust space between Latin and Asian text,
Adjust space between Asian text and numbers
h
* min
h
min
C
R ,eff
Friction force parameter:
f
*
FSo
f
eff
Formatted: Font: 11 pt
ℎ
min
∗
Formatted: FooterPageNumber, Space Before: 0 pt,
Lubri
...
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